{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 三原子链声子分析\n",
    "\n",
    "<img src=\"atom3chain.png\" alt=\"\" style=\"width:40%; display:block; margin:auto;\" />\n",
    "\n",
    "对于这样一个三原子链，原子振动可以通过下面的方程来描述（分别对应图中一个晶体单元内的三个原子）：\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "M_1 \\omega^2 A_1 \\exp[ikr_1] &= (D_{12} + D_{13})A_1 \\exp[ikr_1] - D_{12}A_2 \\exp[ikr_2] - D_{13}A_3 \\exp[ik(r_3 - a)] \\\\\n",
    "M_2 \\omega^2 A_2 \\exp[ikr_2] &= -D_{21}A_1 \\exp[ikr_1] + (D_{21} + D_{23})A_2 \\exp[ikr_2] - D_{23}A_3 \\exp[ikr_3] \\\\\n",
    "M_3 \\omega^2 A_3 \\exp[ikr_3] &= -D_{31}A_1 \\exp[ik(r_1 + a)] - D_{32}A_2 \\exp[ikr_2] + (D_{31} + D_{32})A_3 \\exp[ikr_3]\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "由于原子质量系数的存在，这并不是一个关于振幅 $ A_i $ 的标准的特征值问题。\n",
    "为了能够变成一个标准的特征值问题，需要对原子质量系数进行处理，\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\omega^2 \\sqrt{M_1} A_1 \\exp(ikr_1) &= \\frac{D_{12} + D_{13}}{M_1} \\sqrt{M_1} A_1 \\exp(ikr_1) - \\frac{D_{12}}{\\sqrt{M_1 M_2}} \\sqrt{M_2} A_2 \\exp(ikr_2) - \\frac{D_{13}}{\\sqrt{M_1 M_3}} \\sqrt{M_3} A_3 \\exp[ik(r_3 - a)] \\\\\n",
    "\\omega^2 \\sqrt{M_2} A_2 \\exp(ikr_2) &= - \\frac{D_{21}}{\\sqrt{M_2 M_1}} \\sqrt{M_1} A_1 \\exp(ikr_1) + \\frac{D_{21} + D_{23}}{M_2} \\sqrt{M_2} A_2 \\exp(ikr_2) - \\frac{D_{23}}{\\sqrt{M_2 M_3}} \\sqrt{M_3} A_3 \\exp(ikr_3) \\\\\n",
    "\\omega^2 \\sqrt{M_3} A_3 \\exp(ikr_3) &= - \\frac{D_{31}}{\\sqrt{M_3 M_1}} \\sqrt{M_1} A_1 \\exp[ik(r_1 + a)] - \\frac{D_{32}}{\\sqrt{M_3 M_2}} \\sqrt{M_2} A_2 \\exp(ikr_2) + \\frac{D_{31} + D_{32}}{M_3} \\sqrt{M_3} A_3 \\exp(ikr_3)\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "这里作进行替换：$ A^\\prime_1 = \\sqrt{M_1} A_1, \\quad A^\\prime_2 = \\sqrt{M_2} A_2, \\quad A^\\prime_3 = \\sqrt{M_3} A_3 $, 则有：\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\omega^2 A^\\prime_1 \\exp(ikr_1) &= \\frac{D_{12} + D_{13}}{M_1} A^\\prime_1 \\exp(ikr_1) - \\frac{D_{12}}{\\sqrt{M_1 M_2}} A^\\prime_2 \\exp(ikr_2) - \\frac{D_{13}}{\\sqrt{M_1 M_3}} A^\\prime_3 \\exp(ik(r_3 - a)) \\\\\n",
    "\\omega^2 A^\\prime_2 \\exp(ikr_2) &= -\\frac{D_{21}}{\\sqrt{M_2 M_1}} A^\\prime_1 \\exp(ikr_1) + \\frac{D_{21} + D_{23}}{M_2} A^\\prime_2 \\exp(ikr_2) - \\frac{D_{23}}{\\sqrt{M_2 M_3}} A^\\prime_3 \\exp(ikr_3) \\\\\n",
    "\\omega^2 A^\\prime_3 \\exp(ikr_3) &= -\\frac{D_{31}}{\\sqrt{M_3 M_1}} A^\\prime_1 \\exp[i k(r_1 + a)] - \\frac{D_{32}}{\\sqrt{M_3 M_2}} A^\\prime_2 \\exp(ikr_2) + \\frac{D_{31} + D_{32}}{M_3} A^\\prime_3 \\exp(ikr_3)\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "可以看到，这是一个关于 $ A^\\prime_i $ 的标准的特征值问题，也就可以用标准的特征值求解方法来求解：\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "\\frac{D_{12} + D_{13}}{M_1} & -\\frac{D_{12}}{\\sqrt{M_1 M_2}} \\exp[ik(r_2 - r_1)] & -\\frac{D_{13}}{\\sqrt{M_1 M_3}} \\exp[ik(r_3 - r_1 - a)] \\\\\n",
    "-\\frac{D_{21}}{\\sqrt{M_2 M_1}} \\exp[ik(r_1 - r_2)] & \\frac{D_{21} + D_{23}}{M_2} & -\\frac{D_{23}}{\\sqrt{M_2 M_3}} \\exp[ik(r_3 - r_2)] \\\\\n",
    "-\\frac{D_{31}}{\\sqrt{M_3 M_1}} \\exp[ik(r_1 - r_3 + a)] & -\\frac{D_{32}}{\\sqrt{M_3 M_2}} \\exp[ik(r_2 - r_3)] & \\frac{D_{31} + D_{32}}{M_3}\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "A^\\prime_1 \\\\\n",
    "A^\\prime_2 \\\\\n",
    "A^\\prime_3\n",
    "\\end{bmatrix} = \\omega^2\n",
    "\\begin{bmatrix}\n",
    "A^\\prime_1 \\\\\n",
    "A^\\prime_2 \\\\\n",
    "A^\\prime_3\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "相应的行列式表达为：\n",
    "\n",
    "$$\n",
    "\\begin{vmatrix}\n",
    "\\omega^2 - \\frac{D_{12} + D_{13}}{M_1} & \\frac{D_{12}}{\\sqrt{M_1 M_2}} \\exp[ik(r_2 - r_1)] & \\frac{D_{13}}{\\sqrt{M_1 M_3}} \\exp[ik(r_3 - r_1 - a)] \\\\\n",
    "\\frac{D_{21}}{\\sqrt{M_2 M_1}} \\exp[ik(r_1 - r_2)] & \\omega^2 - \\frac{D_{21} + D_{23}}{M_2} & \\frac{D_{23}}{\\sqrt{M_2 M_3}} \\exp[ik(r_3 - r_2)] \\\\\n",
    "\\frac{D_{31}}{\\sqrt{M_3 M_1}} \\exp[ik(r_1 - r_3 + a)] & \\frac{D_{32}}{\\sqrt{M_3 M_2}} \\exp[ik(r_2 - r_3)] & \\omega^2 - \\frac{D_{31} + D_{32}}{M_3}\n",
    "\\end{vmatrix}\n",
    "= 0\n",
    "$$\n",
    "\n",
    "由此可以导出特征方程。经过一系列推导，可以得到一个关于 $ x = \\omega^2 $ 的三次多项式方程：\n",
    "\n",
    "$$ P_3 x^3 + P_2 x^2 + P_1 x + P_0 = 0 $$\n",
    "\n",
    "其中 $ P_3, P_2, P_1, P_0 $ 分别为：\n",
    "\n",
    "- $P_3 = 1$\n",
    "\n",
    "- $P_2 = -\\left(\\frac{D_{12} + D_{13}}{M_1} + \\frac{D_{21} + D_{23}}{M_2} + \\frac{D_{31} + D_{32}}{M_3}\\right)$\n",
    "\n",
    "- $P_1 = \\left(\\frac{(D_{12} + D_{13})(D_{21} + D_{23})}{M_1 M_2} + \\frac{(D_{21} + D_{23})(D_{31} + D_{32})}{M_2 M_3} + \\frac{(D_{31} + D_{32})(D_{12} + D_{13})}{M_3 M_1}\\right) - \\left(\\frac{D_{23} D_{32}}{M_2 M_3} + \\frac{D_{13} D_{31}}{M_1 M_3} + \\frac{D_{12} D_{21}}{M_1 M_2}\\right)$\n",
    "\n",
    "- $P_0 = -\\frac{D_{12} + D_{13}}{M_1} \\frac{D_{21} + D_{23}}{M_2} \\frac{D_{31} + D_{32}}{M_3} + 2 \\cos(ka) \\frac{D_{12}D_{23}D_{31}}{M_1M_2M_3} + \\left( \\frac{D_{12} + D_{13}}{M_1} \\frac{D_{23}D_{32}}{M_2M_3} + \\frac{D_{21} + D_{23}}{M_2} \\frac{D_{13}D_{31}}{M_1M_3} + \\frac{D_{31} + D_{32}}{M_3} \\frac{D_{12}D_{21}}{M_1M_2} \\right)$\n",
    "\n",
    "考虑到 $ D_{ij} = D_{ji} $，可以进一步化简上面的系数为：\n",
    "\n",
    "- $P_3 = 1$\n",
    "\n",
    "- $P_2 = -\\left( \\frac{D_{12} + D_{13}}{M_1} + \\frac{D_{21} + D_{23}}{M_2} + \\frac{D_{31} + D_{32}}{M_3} \\right)$\n",
    "\n",
    "- $P_1 = (D_{12}D_{23} + D_{13}D_{21} + D_{13}D_{23}) \\left( \\frac{1}{M_1 M_2} + \\frac{1}{M_2 M_3} + \\frac{1}{M_1 M_3} \\right)$\n",
    "\n",
    "- $P_0 = -4 \\sin^2\\left(\\frac{ka}{2}\\right) \\frac{D_{12} D_{23} D_{31}}{M_1 M_2 M_3}$\n",
    "\n",
    "### 对称三原子链简化模型\n",
    "\n",
    "当其中两层原子一样时，可以假设 $D_{12} = D_{13} = D$，$D_{23} = \\alpha D$，$M_1 = M$，$M_2 = M_3 = \\frac{M}{\\beta}$，从而得到：\n",
    "\n",
    "- $P_3 = 1$\n",
    "\n",
    "- $P_2 = -2(1 + \\beta + \\alpha \\beta) \\frac{D}{M}$\n",
    "\n",
    "- $P_1 = (\\beta + 2\\alpha \\beta)(\\beta + 2) \\frac{D^2}{M^2}$\n",
    "\n",
    "- $P_0 = -4 \\sin^2\\left(\\frac{ka}{2}\\right) \\alpha \\beta^2 \\frac{D^3}{M^3}$\n",
    "\n",
    "通过令 $X = \\frac{M}{D} x$（即 $x = \\frac{D}{M} X$），特征方程转化为：\n",
    "\n",
    "$$\n",
    "X^3 - 2(1 + \\beta + \\alpha \\beta)X^2 + (\\beta + 2\\alpha \\beta)(\\beta + 2)X - 4 \\sin^2\\left(\\frac{ka}{2}\\right) \\alpha \\beta^2 = 0\n",
    "$$\n",
    "\n",
    "基于该特征方程，我们作两个特殊化的考虑：\n",
    "\n",
    "#### 1. $ k = 0 $ (即 Gamma 点)\n",
    "\n",
    "\n",
    "令 $ k = 0 $, $ P_0 = 0 $, 显然 $ X = 0 $ 是一个根，对应才材料的声学支。\n",
    "当 $ X \\neq 0 $ 时，方程的解为：\n",
    "\n",
    "$$\n",
    "X^2 - 2(1 + \\beta + \\alpha \\beta)X + (\\beta + 2\\alpha \\beta)(\\beta + 2) = 0 \\\\\n",
    "$$\n",
    "\n",
    "分解因式得到：\n",
    "\n",
    "$$\n",
    "[X - (\\beta + 2\\alpha \\beta)][X - (\\beta + 2)] = 0\n",
    "$$\n",
    "\n",
    "有 $ X_1 = \\beta + 2\\alpha \\beta $, $ X_2 = \\beta + 2 $。\n",
    "\n",
    "注意到，当 $ \\alpha \\beta = 1 $ 时，有 $ X_1 = X_2 = \\beta + 2 $。\n",
    "此时，两个光学支的频率相等，光学-光学支带隙为0；而且，$ \\beta $ 越大，该简并点的频率越高。\n",
    "\n",
    "\n",
    "#### 2. $ k = \\frac{\\pi}{a} $ (布里渊区边界)\n",
    "\n",
    "令 $ k = \\frac{\\pi}{a} $, 则 $ \\sin^2\\left(\\frac{ka}{2}\\right) = 1 $,\n",
    "此时 $ P_0 = -4 \\alpha \\beta^2 $，特征方程为：\n",
    "\n",
    "$$ X^3 - 2(1 + \\beta + \\alpha \\beta)X^2 + (\\beta + 2\\alpha \\beta)(\\beta + 2)X - 4 \\alpha \\beta^2 = 0 $$\n",
    "\n",
    "可以验证 $ X = \\beta $ 是一个根，对其进行因式分解，有：\n",
    "\n",
    "$$\n",
    "(X - \\beta)[X^2 - (2 + \\beta + 2\\alpha \\beta)X + 4\\alpha \\beta] = 0\\\\\n",
    "(X - \\beta)[(X - \\beta)(X - 2 - 2\\alpha \\beta) - 2\\beta(1 - 2\\alpha + \\alpha \\beta)] = 0\\\\\n",
    "$$\n",
    "\n",
    "如果再有 $ 1 - 2\\alpha + \\alpha \\beta = 0 $，则 $ \\beta $ 成为该方程的重根。\n",
    "此时，最低能的两个声子支能量相等，声学-光学带隙为0。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def phonoline(alpha, beta):\n",
    "    Cij = np.array([\n",
    "        [2.0, -1.0, -1.0],\n",
    "        [-1.0, 1+alpha, -alpha],\n",
    "        [-1.0, -alpha, 1+alpha],\n",
    "    ])\n",
    "    Mass = np.array([1.0, 1/beta, 1/beta])\n",
    "    \n",
    "    r = np.array([0, 1/3, 2/3])   # position of atoms\n",
    "    \n",
    "    q = np.arange(-1/2, 1/2+1e-10, 1/100)\n",
    "    Dij = np.zeros([len(q), 3, 3], dtype=complex)\n",
    "    Dij[:, 0, 0] = Cij[0, 0]/Mass[0]\n",
    "    Dij[:, 1, 1] = Cij[1, 1]/Mass[1]\n",
    "    Dij[:, 2, 2] = Cij[2, 2]/Mass[2]\n",
    "\n",
    "    Dij[:, 0, 1] = Cij[0, 1]/np.sqrt(Mass[0]*Mass[1])*np.exp(1j*2*np.pi*q*(r[1]-r[0]))\n",
    "    Dij[:, 0, 2] = Cij[0, 2]/np.sqrt(Mass[0]*Mass[2])*np.exp(1j*2*np.pi*q*(r[2]-r[0]-1))\n",
    "    Dij[:, 1, 2] = Cij[1, 2]/np.sqrt(Mass[1]*Mass[2])*np.exp(1j*2*np.pi*q*(r[2]-r[1]))\n",
    "\n",
    "    Dij[:, 1, 0] = Cij[1, 0]/np.sqrt(Mass[0]*Mass[1])*np.exp(1j*2*np.pi*q*(r[0]-r[1]))\n",
    "    Dij[:, 2, 0] = Cij[2, 0]/np.sqrt(Mass[0]*Mass[2])*np.exp(1j*2*np.pi*q*(r[0]-r[2]+1))\n",
    "    Dij[:, 2, 1] = Cij[2, 1]/np.sqrt(Mass[1]*Mass[2])*np.exp(1j*2*np.pi*q*(r[1]-r[2]))\n",
    "\n",
    "    val, vec = np.linalg.eigh(Dij)\n",
    "    return q, val, vec"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 当 $ \\alpha \\beta = 1 $ 时，O-O 带隙恰好为 0。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "alpha, beta = 3, 1/3\n",
    "q, val, _ = phonoline(alpha, beta)\n",
    "val[(val < 0) & (val > -1E-6)] = 0\n",
    "\n",
    "plt.scatter(q, np.sqrt(val[:, 0]), marker='o')\n",
    "plt.scatter(q, np.sqrt(val[:, 1]), marker='o')\n",
    "plt.scatter(q, np.sqrt(val[:, 2]), marker='o')\n",
    "plt.xlabel('q')\n",
    "plt.ylabel('Energy')\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 当 $ 1 - 2\\alpha + \\alpha \\beta = 0 $ 时， A-O 带隙为0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DAABsheQGAADYCskNAACwFZIbAABgKyQ3AADAVkhuAACArZDcAAAAWyG5AQAAtmJpcvPxxx+rf//+at68uRwOh95+++1a77N69Wp16dJFSUlJuuKKKzR//vyIjxMAAMQOS5ObkpISdezYUbNmzfLr/N27d6tfv366/vrrtWXLFj3wwAO6++67tXz58giPFAAAxIo6Vv7yvn37qm/fvn6fP3v2bF122WV6/vnnJUnt2rXTp59+qhdeeEF9+vSJ1DABAEAMsTS5CVR+fr5ycnIqHevTp48eeOCBau9TVlamsrIy7+3i4mJJksvlksvlisg4Y4knBsQisoizOYizeYi1OYjzWYHEIKaSm4KCAqWnp1c6lp6eruLiYp08eVL16tWrcp9p06ZpypQpVY6vWLFCKSkpERtrrMnLy7N6CHGBOJuDOJuHWJuDOEulpaV+nxtTyU0wJkyYoNzcXO/t4uJiZWZmqnfv3kpNTbVwZNHB5XIpLy9PvXr1ktPptHo4tkWczUGczUOszUGcz/LMvPgjppKbjIwMFRYWVjpWWFio1NRUn1UbSUpKSlJSUlKV406nM+5fKOciHuYgzuYgzuYh1uYgzgro+cfUOjfZ2dlatWpVpWN5eXnKzs62aEQAACDaWJrcnDhxQlu2bNGWLVskVVzqvWXLFu3du1dSxZTS0KFDveffc889+uabb/Twww9r27Zteumll/Tmm29q3LhxVgwfAABEIUuTmw0bNqhz587q3LmzJCk3N1edO3fWxIkTJUkHDhzwJjqSdNlll+n9999XXl6eOnbsqOeff16vvPIKl4EDAAAvS3tuevbsKcMwqv25r9WHe/bsqc2bN0dwVAAAIJbFVM8NAABAbUhuAACArZDcAAAAWyG5AQAAtkJyAwAAbIXkBgAA2ArJDQAAsBWSGwAAYCskNwAAwFZIbgAAgK2Q3AAAAFshuQEAALZCcgMAAGyF5AYAANgKyQ0AALAVkhsAAGArJDcAAMBWSG4AAICtkNwAAABbqWP1AACgCne59O0a6UShVD9dysyS/rPu7O1Lr6047/xzvl175ni+dHkP3+fU9jiXXislJJr/nAGEDckNgMg5P0mpLik5N+EoPSItnyAV7z/7OI4EyXCfvV2vsSSHdPJo5XMcdaWOf5QW3iYl1fN9Tm2P06CZ1HW4dGEr/8dMQgRElaCSm5KSEl1wwQXhHguAaBZoNeXILmnT/MpJSnVJybkJhy/n//zkd77PcfhxTm2Pc/yAtPqpwMac2lzqPU264EKqREAUCCq5SU9P18CBAzVixAj96Ec/CveYAFjt/EQm2GrK+fxJOKKNP2Mu3i8tHlb5WLBVIpIdIGRBJTcLFizQ/PnzdcMNN6hly5YaMWKEhg4dqubNm4d7fADCrbapIl8VF1/8qYLEs2CqRL4qQFR8gIAFldwMGDBAAwYM0KFDh/SnP/1J8+fP1xNPPKE+ffpoxIgRuvnmm1WnDu08QFQ4N5nxd6oI1vBVAaLiAwQspAzkoosuUm5urnJzc/W73/1ODz30kJYuXaq0tDTdc889Gj9+vFJSUsI1VgDnq60Pxtd00vmouES3YCs+ND0jjoWU3BQWFuq1117T/Pnz9e233+rWW2/VyJEj9d///ldPP/201q5dqxUrVoRrrEB8C6YPBvHBn56f6qa8SHhgQ0ElN3/729/06quvavny5Wrfvr1Gjx6tO+64Q40aNfKec+2116pdu3bhGicQf2qbTvKFxAYe/jQ9M70FmwoquRk+fLj+53/+R5999pl++MMf+jynefPmeuyxx0IaHBA3/KnKxLMqVx41qfjv+Zdnn6u6c2p7nHjib0MzCQ9iTFDJzYEDB2rtpalXr54mTZoU1KAA2wumKmMH/iQcqS2k3k8FvmZMZpa0Z630xXfS4LeCW6HYZ8O1H2O2C6o7sImgkpvTp0+ruLi4ynGHw6GkpCTVrVs35IEBtuEur9gOQKr4b9lRe1Rl/KmCNGgudb0rPKv9XnZd7ccuzZa+WFrxX89jnH9ObY/z4wcjtKpyjFaJqqvuJJ95Pp6tLkh4EEWCSm4aNWokh8NR7c8vvvhi3XXXXZo0aZISEtibE3HGV1XmxNGz2wK4v7d6hIELtprib6LiK+GwSkKif4nU+bfb9Q+9ShQLPNWdhOSzr+kLGlPdQVQJKrmZP3++HnvsMd11113q3r27JGn9+vV67bXX9Pjjj+vQoUN67rnnlJSUpEcffTSsAwaiir+9MgnJ1ozPH/5WXIKtpsQLX0lRoFUiX6+fWKj40LuDKBNUcvPaa6/p+eef18CBA73H+vfvrw4dOugPf/iDVq1apUsuuUS/+c1v/EpuZs2apWeffVYFBQXq2LGjfve733mTJl9mzpypl19+WXv37lVaWppuvfVWTZs2TcnJUfwBAvv58l1p2SOx983bn6kiPojM4SshOr8CFIsVH1+9O6nNpZueltrfbM2YEFeCSm7WrFmj2bNnVzneuXNn5edX9Bb86Ec/0t69e2t9rEWLFik3N1ezZ89WVlaWZs6cqT59+mj79u1q2rRplfMXLlyo8ePHa968ebr22mu1Y8cO3XXXXXI4HJoxY0YwTwfwn6dSs32ptPYlq0dTlT/NuYFUYWA+f6bF/Kn4RFvTc/F+6c07pWtGS21+SgKNiAoqucnMzNTcuXM1ffr0Ssfnzp2rzMxMSdKRI0fUuHHjWh9rxowZGjVqlIYPHy5Jmj17tt5//33NmzdP48ePr3L+mjVr1KNHDw0ePFiS1LJlSw0aNEjr1q3z+fhlZWUqKyvz3vY0QrtcLrlcLj+erb15YkAsfHCXS/9ZL5UclC5oWjEtsHJyRQleCmiqyXXmXFc4p6caNJdunCSlNDk7xhZdpX0bz97O7F71A6TcXfHHhuLq9XzxNZVvX3FT5dfr+a+F81+/IQr6Nb1+XsWfBs2kGydXfv36er3Gubh6TdcikBg4DMMwAv0F7777rm677Ta1bdvWu87Nhg0btG3bNi1evFg/+9nP9PLLL+vrr7+usZpy6tQppaSkaPHixRowYID3+LBhw3Ts2DG98847Ve6zcOFCjR49WitWrFD37t31zTffqF+/frrzzjt9ToFNnjxZU6ZM8fk4bA0BAEBsKC0t1eDBg1VUVKTU1NQazw0quZGkPXv26A9/+IO2b98uSWrTpo3+93//Vy1btvT7Mfbv368WLVpozZo1ys7O9h5/+OGH9dFHH1Vbjfntb3+rBx98UIZh6PTp07rnnnv08ssv+zzXV+UmMzNThw8frjU48cDlcikvL0+9evWS0+m0ejjmqa0qE2auhGTldfitem29T05/rpbyVZXhW22t4vb1HKwQ/h0E/JoOBtUdXtPnKC4uVlpaml/JTcDTUi6XSzfddJNmz56tadOmBT3IYK1evVpPPfWUXnrpJWVlZWnnzp26//77NXXqVD3xxBNVzk9KSlJSUlKV406nM+5fKOeKq3hY2AjsdH/v+4PA36uT4Je4ej2HxCld8ePKh37QP6Dm5Wpf0+FQtFv6G43JEq9pSQE9/4CTG6fTqX//+9+B3s2ntLQ0JSYmqrCwsNLxwsJCZWRk+LzPE088oTvvvFN33323JKlDhw4qKSnRr371Kz322GOsqwPfoqkROJAmX8Bs5zc0V9e8fMKiS9NpTIYfgmoovuOOO3w2FAeqbt266tq1q1atWuXtuXG73Vq1apXGjh3r8z6lpaVVEpjExIoXdpAzbLCbaNunqUFzqcsIqVhntwXgzRixorrL1b/5rGKri+selDbPM//f19qXKv6wpg58CHr7hXnz5mnlypXq2rWrLrjggko/D+SS7NzcXA0bNkzdunVT9+7dNXPmTJWUlHivnho6dKhatGjhnQLr37+/ZsyYoc6dO3unpZ544gn179/fm+Qgjlm99kx1VZlyt7T0vG0BgFiVkHh2q4sfPSD9JNe6LxSsqQMfgkpuPv/8c3Xp0kWStGPHjko/q2lbBl9uv/12HTp0SBMnTlRBQYE6deqkZcuWKT09XZK0d+/eSpWaxx9/XA6HQ48//rj27duniy66SP3799dvfvObYJ4K7CAappxqK5Hb9NJrQFLNixF6/106JJlUXWfqKu4Fldx8+OGHYR3E2LFjq52GWr16daXbderU0aRJk9hxPF5F25RTagvppul8QwTO50l4LrtOuiTbmooqU1dxK6jkxmPnzp3atWuXfvzjH6tevXoyDCPgyg3gt2idcuINEqhZ+5ultv2YuoJpgkpujhw5ooEDB+rDDz+Uw+HQ119/rcsvv1wjR45U48aN9fzzz4d7nIhXVk45cXk2ED617aNl9p5ZTF3ZWlDJzbhx4+R0OrV37161a9fOe/z2229Xbm4uyQ2CY+WUE1UZwHz+XnYeyfcApq5sKajkZsWKFVq+fLkuvvjiSsdbt26tb7/9NiwDQ5yxasqJb21A9LCyMZmpK1sJKrkpKSnxuS/T0aNHfa4GDPhk5ZQTjcBAbLCyMZmpq5gVVHJz3XXX6fXXX9fUqVMlVVz+7Xa79cwzz+j6668P6wBhE0w5AQiVVY3JTF3FnKCSm2eeeUY33nijNmzYoFOnTunhhx/WF198oaNHj+qzzz4L9xgR65hyAhAuTF3BD0ElN1dddZV27Nih3//+92rQoIFOnDihX/7ylxozZoyaNWsW7jEiFjHlBMAsTF3hPEGvc9OwYUM99thj4RwL7MLMSg1TTgDOFQ1TV1RyLBd0cnPs2DGtX79eBw8elNtdeWn5oUOHhjwwxJBz+2mO7JJWT1PEl1nnWxKA6lg6dXWgopLT81HWyLJQUMnNe++9pyFDhujEiRNKTU2ttCqxw+EgubG785MZMxfeYsoJQDBMm7o6kzCtfursoQbNpK7DSXZMFFRy8+tf/1ojRozQU0895fOScNgYU04AYp3ZU1fHD1ROdpi6irigkpt9+/bpvvvuI7GJB0w5AbAjpq5sLajkpk+fPtqwYYMuv/zycI8H0cTsS7iZcgJgJSunrqjmhFVQyU2/fv300EMP6csvv1SHDh3kdDor/fzmm/nLiVlmXcLNlBOAaGb21BWXlIdVUMnNqFGjJElPPvlklZ85HA6Vl5eHNipYw4xKDf9wAcQKK6auzr+kvHXf8D12HAkquTn/0m/EKHe59G1+xf9/OlP66DeKWD8NU04A7MCsqStPX85PHpd0ZcV79eU9+FLop4RATv7pT3+qoqIi7+3p06fr2LFj3ttHjhxR+/btwzY4RNCX70ozr5IW3lZx+5PnFL7E5szSAD0flW6ZKw37u/TAVhIbAPbS/mbpgc8r3uNumVvxnieHvO+BITnzfvzJcxX/XXhbxXv2l++G4bHtL6DKzfLly1VWVua9/dRTT2ngwIFq1KiRJOn06dPavn17WAeIMPLVT5OQHP7fk9qcKg2A+HD+1FXTdhGs5tCX46+AkhvDMGq8jSgWyX6aBs2lrndxSSMAnN+IHImFTtnqoVZBb7+AKBex9WnONM+xPgMA+HZ+NefHD/p4P5ZCfk9mvZxqBZTcOByOSlsteI4hCpi1JQJTTgAQmIhNXbHVQ3UCnpa66667lJSUJEn6/vvvdc899+iCCy6QpEr9ODARl3ADQOw4d+oq3JeUs9WDpACTm2HDhlW6fccdd1Q5h00zTWDmlghcwg0A4Wf2JeVxNnUVUHLz6quvRmoc8FdEqzT00wCA6Xw1IXv7ckIVn1s90FAc7Uyt0tBPAwCWqK4v58TR8P+uOLiknOQmmpm5ceXgt1j9EgCihaea881n0hffnTkY4a0ebPTFNqAVimECd7m0+xNp2YSKzDqSiU1qC+kXf6z4/0uzSWwAIJokJFa8N0sV79WpzSLzezx9OauflrYurvgMcsf2HpFUbqKJFf005W7pm6UR+H0AgLBp+1PpBz+LzHo5NuzLIbmxUjT005SzCSoAxAS2evAbyY1VIt1Pw5YIAGBvbPVQLZIbK3z5rvTmUIV3F24u4QaAuGPqVg9DpYGvx0SCExUNxbNmzVLLli2VnJysrKwsrV+/vsbzjx07pjFjxqhZs2ZKSkrSlVdeqaVLY6BvxF0u7VotvXefwjr9lNpcGvgnqecjUodbK17oJDYAEH88yU6HWys+Ewa+HqZGZKPiz9/HSf9+M+qbji2v3CxatEi5ubmaPXu2srKyNHPmTPXp00fbt29X06ZNq5x/6tQp9erVS02bNtXixYvVokULffvtt2rUqJH5gw9E2KahqNIAAPwU7q0eSg9LfxtV8f9RPFVleXIzY8YMjRo1SsOHD5ckzZ49W++//77mzZun8ePHVzl/3rx5Onr0qNasWSOn0ylJatmypZlD9k+kmoVZaA8AEIhIbfUQxU3HliY3p06d0saNGzVhwgTvsYSEBOXk5Cg/P9/nfd59911lZ2drzJgxeuedd3TRRRdp8ODBeuSRR5SYWDWoZWVllTb0LC4uliS5XC65XK4wP6Mzti2VVk6q2MDMIyEptMf84SipdW8ps3vFiydMY/fEIGKxgCTibBbibB5ibY6wx7l1X6lVb+k/66WSg9LR3dInz5/5YZBfwNfPq/jToJmUM6XisvUICCQGDsMwInTtce3279+vFi1aaM2aNcrOzvYef/jhh/XRRx9p3bp1Ve7Ttm1b7dmzR0OGDNHo0aO1c+dOjR49Wvfdd58mTZpU5fzJkydrypQpVY4vXLhQKSkp4X1CAAAgIkpLSzV48GAVFRUpNTW1xnMtn5YKlNvtVtOmTfXHP/5RiYmJ6tq1q/bt26dnn33WZ3IzYcIE5ebmem8XFxcrMzNTvXv3rjU4/vr3qoXKWD9dTRXqHiBn5kGve1Bqcpl0QdOzlZoIcblcysvLU69evbzTfAg/4mwO4mweYm0O0+LsLq+o5ny9QvrnHAXbl2OcuafHQTVRQffxuvrGwSEP0TPz4g9Lk5u0tDQlJiaqsLCw0vHCwkJlZGT4vE+zZs3kdDorTUG1a9dOBQUFOnXqlOrWrVvp/KSkJCUlVZ0ScjqdYXmhbF7+mjrn3ydJSnDUcnJtUltY1k8TrnigZsTZHMTZPMTaHJGPs1O64scVfy7tHra+nGbGfjXLv0//ckid+wwLbYQBPH9LLwWvW7euunbtqlWrVnmPud1urVq1qtI01bl69OihnTt3yu0+u7Lujh071KxZsyqJTaSVnz6t5vkVU14hJTb1GktD35Ue2EqjMADAWu1vlh74XBr2d+mXc6SUNFWux/jP89nYLH+Kyk+fDt8Ya/u9pv2mauTm5mrOnDl67bXX9NVXX+nee+9VSUmJ9+qpoUOHVmo4vvfee3X06FHdf//92rFjh95//3099dRTGjNmjOlj37ZuudJ1JOjExpBDkkPq/1vp8p9ETZc5ACDOea6wunqg9LMXJHk+s4J4KIeUoSPatm55OEdYI8t7bm6//XYdOnRIEydOVEFBgTp16qRly5YpPT1dkrR3714lJJzNwTIzM7V8+XKNGzdOV199tVq0aKH7779fjzzyiOljP/ndvoDONwzJcc5ro1BNdCB7kjpTrQEARKv2N2tz9otqnj9F6ToS9MME+pkZCsuTG0kaO3asxo4d6/Nnq1evrnIsOztba9eujfCoalevcQu/z3Wf6cua4bpF3xrNdFCNtN7dVu4PEzTy1BfKaZ+h7pc1UWLIjTsAAISm3G1o/e6jOnj8e+05XKqZH6bJoRfVPWGbchwbNbLOP2QosJaMQD4zQxUVyU2sapvVR4V5F+oio/apqQJdqCmuO7Xc3b3Kz+Z+tkdzP9ujZg2TNal/e910VTiWygYAIHDLPj+gKe99qQNF31c6bihBa93ttVbt9U+jjSY5X1fzc64SPn92wsNtSAcdF6ptVp9ID92L5CYEiXXqaH/2JF205j65jcoZrKdSM6/8Jq10d6uo0tTS4lRQ9L3uWbBJ43Jaq2XaBWraIJlqDgAg4jyVmrwvCzTvsz21nr/c3V15Zd3UPWGbmuqYLnUUaFydxTKq+Sw8kD1JGXXMSzlIbkLUuc8wbZaqzEXWVKmpjmdFgRdWfu09RjUHABBJ1VVqauM+U8nx2GFcXKWac9BxYUVvaYiXgQeK5CYMOvcZpvIbh+iLdcu1becOvbX9tP7pbqvyMFyMVlD0ve5dsEkv39GFBAcAEFbLPj+gexdsCsfOh1pxpprzTLcTapl8XPUat1DbrD6mVmw8SG7CJLFOHf2gRz/9oEc/XfD5AX0bRBbsi+cFN/6vW9Ug2alrLr+QaSoAQNA8U1AFRSc19f2vwpLYSFJGFM00kNxEwE1XNVOv9hmVO81X7pAU/L7gx066NOSVdUxTAQCCFuwUVE1G9mgZdVf8ktxESGKCQ9mtLvTebpNRPywvKJqOAQCBCLRZ2F/R/GWb5MYk51ZzPC+wYLYlo+kYAOCvcFVqPJ9XsfLFmuTGRJ5qTnarC9X9siZhKw1SzQEASD4W31u5Iyw9NdHUT+MPkhuLhLMvh2oOACBe+mn8QXJjoUj15UjSgTPVnFh9YQIAaheP/TT+ILmJIp5qztpdRzRm4SYdO+kK+THZ2gEA7CnclZomFzj1xM9+oIzU2G9tCH2VOYRVYoJDPVqnafotHeSQgtxgvirPYoDLPj8QpkcEAFjFs/heOBIbz2fNU7/ooF90bqHsVrG/nhrJTZS66apmevmOLspomByWxzPO/Hl0yVYt2bxP+buOqNwdrqWbAACRVu42lL/riJZs+q8eXfJ5WBffs9sq+ExLRbFILAZ4tMSlcYu2SKqYU53Yr014BgsAiJiVXxXqyfe30yzsJ5KbKBfppuMHFm3RM92l9buP6pormtruBQ4AscrTLCxJDyzaorLy8Lw/x0MPJslNjIlENUeSRrz2TzWpX8/2L3gAiAWeZuGjJ07qme7BP06sLb4XLiQ3MYitHQDAXqpbfC8pMbTHjbXF98KF5MYG2NoBAGIXi++FH8mNTURya4d7F2yyXSc9AEQDzyXd4bryiS+kFUhubOjcSk5B0UlNff8rfVdyKqh/PJ77jP/rVjVIduqay2N//QMAsFq529DaXUc0/q9bQ05s7LT4XriQ3NjUuX059eom6t4Fm4KaqvI4dtKlIa+s41sBAIQonDt1SxWL7/GeXBnJTRzwLAhI0zEAmI+dus1HchMnqms6DhRNxwDgP5qFrUFyE0d8NR0fPXEy5MdlB3IAOIuduq1HchOnvDuQ7zyow1+t1ZieV+iFVbskBd+Xww7kAOJdOPtpDEljeraSSndo3rAfsop8ANg4M44lJjjU/bImkqR7e7YK20ad7EAOIB6Fc6fujIbJmn1HF93b8wpJoiIeICo38PJWc3Yd0ZiFm3TspCuox/FUfh5dslUnXW4uTwRgW54pKM+yG6E2Cjeq59SsIV28y264XMG9D8c7khtUkpjgUI/WaZp+Swfdu2CTpPDtQM5UFQA7CWezsOer3/RbOqjHFWkhP168Y1oKPnkuHw/HNJV0tul46ntfKH/XEZW7w7UeJwCYp9xtKH/XET353he6J0xTUFLFNBQrwYcPlRtUKxI7kNN0DCBWhbtZmPXCIofkBjWK5A7k7FkFIFaEcw8oFt+LPJIbBCTcO5DTdAwgWoW7WZi1wMwTFT03s2bNUsuWLZWcnKysrCytX7/er/u98cYbcjgcGjBgQGQHiEo81ZyJ/X+g2SH25XiajgfNWasfPf0Bl48DiArLPj+gHz39gQbNWatxb/5LR0tOBf1Yzc5c1v1E/x8ouxWbD5vB8srNokWLlJubq9mzZysrK0szZ85Unz59tH37djVt2rTa++3Zs0cPPvigrrvuOhNHi/OFcwdyVjoGYKVwrizMTt3Wsjy5mTFjhkaNGqXhw4dLkmbPnq33339f8+bN0/jx433ep7y8XEOGDNGUKVP0ySef6NixY9U+fllZmcrKyry3i4uLJUkul4v1AyRvDEKNRbdLUiWlKrmOvJd/B1vCXbB2txas3a2M1GSN79tWOe3SQxpbNAhXnFEz4mweu8V65VeFmv6PbSoorugnTEoM7nE8Kcxvft5eOe0qvqC7y0/LXR7c49ktzqEIJAYOwzAsuyb31KlTSklJ0eLFiytNLQ0bNkzHjh3TO++84/N+kyZN0r///W8tWbJEd911l44dO6a3337b57mTJ0/WlClTqhxfuHChUlJSwvE0AABAhJWWlmrw4MEqKipSampqjedaWrk5fPiwysvLlZ5e+Zt5enq6tm3b5vM+n376qebOnastW7b49TsmTJig3Nxc7+3i4mJlZmaqd+/etQYnHrhcLuXl5alXr15yOp1he9xyt6GN336nD7cd1J/WfRtU07FH4xSnHrmpnZo2SFLXSxvHZHk3UnFGZcTZPLEea8971MHi7/X08u36rjT4nhpJGpp1qXq2bRr296hYj3M4eWZe/GH5tFQgjh8/rjvvvFNz5sxRWpp/KzgmJSUpKSmpynGn0xn3L5RzhTseTkk9rkxXjyvT1e3ytJAuHy84flrj3toqKfZXOuZ1Zw7ibJ5YjLXv9WqCS0jMek+KxTiHWyDP39LkJi0tTYmJiSosLKx0vLCwUBkZGVXO37Vrl/bs2aP+/ft7j7ndbklSnTp1tH37drVq1Sqyg0bAaDoGYDWaheOLpclN3bp11bVrV61atcrbc+N2u7Vq1SqNHTu2yvlt27bV1q1bKx17/PHHdfz4cb344ovKzMw0Y9gIwrmLAdarm6h7F2wKaaqKlY4B+CucKwtL0lO/6MB7TpSzfFoqNzdXw4YNU7du3dS9e3fNnDlTJSUl3qunhg4dqhYtWmjatGlKTk7WVVddVen+jRo1kqQqxxG9PPtWsdIxgEhjZeH4ZHlyc/vtt+vQoUOaOHGiCgoK1KlTJy1btszbZLx3714lJETFWoMII1Y6BhAprCwMy5MbSRo7dqzPaShJWr16dY33nT9/fvgHBFN4pqqyW12o7pc1CamS41npWIr9pmMAwQvXFJTEe0ksi4rkBqDpGECwaBbG+UhuEDVoOgYQKJqF4QvNLIhKnqbjUDbl9PA0HbMpJ2AvnmbhcExBZTRM5sIEG6Fyg6hF0zGA89EsDH+Q3CCq0XQMwINmYfiL5AYxg6ZjIP7QLIxgkNwgptB0DMQPmoURLBqKEbNoOgbsi2ZhhILKDWIaTceAfdAsjHAhuUHMo+kYiH00CyOcSG5gKzQdA7GDZmFECskNbIemYyD60SyMSKKhGLZG0zEQfWgWRqRRuYHt0XQMWI9mYZiJ5AZxgaZjwDo0C8NsJDeIO+FsOvZMVVEWB3zzTEGFUqmhWRiBIrlBXApX07Hn/PF/3aoGyU5dc/mFvPECqpiGWrvriMb/dWvQiQ3NwggWDcWIe+FoOj520qUhr6zTj57+gIZjxL1lnx/Qj57+QEPmrtOxk66gH4dmYQSLyg2g8DUdF5xZG2dcTmu1TLtATRtUlNEBO/M0Cx88/r32HC7VzJU7QpqGolkYoSK5Ac4IR9Ox5w39hZVfe481a5isif3ahHGkQPRY+VWhnnx/O83CiCokN4AP4W46Hrdoi57uHvZhApYbt2iLvi8PvrpCszAigeQGqEY4m44991n7zRFd2zqdN3DENE+zsBT8yt80CyOSaCgG/BCulY7vfn0DTceIaZ5m4bv/tCGkx6FZGJFE5Qbwk2eqau2uIxqzcFPQV4FU13RMNQfRqLpm4aTE4B6vUT2nZg3pwrIJiCiSGyAAiQkO9Widpum3dNC9CzZJCn5tnPObjmmkRLQJ58rCnjRm+i0d1OOKtJAfD6gJ01JAEMK5IafEppyIPuHc3FJiGgrmonIDBOncK6rOLdlLrHSM2BWulYUNialXWIbkBgjBuVdUSVKbjPohlfE9Kx0zTQUrhGsaKoPXLyxGcgOEUTibjtmQE2YKxwaXNAsjWtBzA4TZuU3HDp1tpAyEZ22cR5ds1ZLN+5S/64jK3aF87ABVlbsN5e86oiWb/qtHl3we0jSUQ2ebhUlsYDUqN0CEeJqOp7z3pY6eOBnUYxwtcWncoi2SuKIK4RXOK6GYhkK0IbkBIsg7TbXzoA5/tVZjel6hF1btkhR40/GBM+vjsKkgguVZs8azOWwwPM3CY3q2kkp3aN6wH+qaK5ryWkRUiYppqVmzZqlly5ZKTk5WVlaW1q9fX+25c+bM0XXXXafGjRurcePGysnJqfF8wGqJCQ7vzuD39mwV8iXkcz/bo0Fz1rLSMQLiWVl40Jy1QSc2UkWVZvYdXXRvzyskiSQbUcny5GbRokXKzc3VpEmTtGnTJnXs2FF9+vTRwYMHfZ6/evVqDRo0SB9++KHy8/OVmZmp3r17a9++fSaPHAjOTVc106eP3KA/j8xSo3rOoB+HtXHgr3CsWdOonlN/vjtLnz5yA9NPiHqWJzczZszQqFGjNHz4cLVv316zZ89WSkqK5s2b5/P8P//5zxo9erQ6deqktm3b6pVXXpHb7daqVatMHjkQPJqOEWk0CyOeWdpzc+rUKW3cuFETJkzwHktISFBOTo7y8/P9eozS0lK5XC41adLE58/LyspUVlbmvV1cXCxJcrlccrmCu0zXTjwxIBaRVV2cb2yTppcGd9T0f2xTQXFw36pLvj+l8Ys3S5IyUpM1vm9b5bRLD23AMYrXc4WVXxVWeU0FuxeU5zV1Y5u0SnEl1uYgzmcFEgOHYRiWfdXbv3+/WrRooTVr1ig7O9t7/OGHH9ZHH32kdevW1foYo0eP1vLly/XFF18oOblqH8PkyZM1ZcqUKscXLlyolJSU0J4AAAAwRWlpqQYPHqyioiKlpqbWeG5MXy01ffp0vfHGG1q9erXPxEaSJkyYoNzcXO/t4uJib59ObcGJBy6XS3l5eerVq5eczuD7P1CzQOK88qtC7+XfoX7ziLdKTry+nn1VaoLhmXB64fZOtb5m4jXWZiPOZ3lmXvxhaXKTlpamxMREFRYWVjpeWFiojIyMGu/73HPPafr06Vq5cqWuvvrqas9LSkpSUlJSleNOpzPuXyjnIh7m8CfOfa++WI6ExLCsQbL3uzKNXvivuFvpOJ5ez8s+P6DRC/91JhEOrR8mmLWU4inWViLOCuj5W5rc1K1bV127dtWqVas0YMAASfI2B48dO7ba+z3zzDP6zW9+o+XLl6tbt24mjRYwz7mbcnrWJPGsLxIIz/mPLtmqky63MlLZwNAOPOvVFBSd1NT3vwq5wsfaSbAby6elcnNzNWzYMHXr1k3du3fXzJkzVVJSouHDh0uShg4dqhYtWmjatGmSpKeffloTJ07UwoUL1bJlSxUUFEiS6tevr/r161v2PIBw82zKmd3qQnW/rElIlRxWOraPcK4szGsBdmV5cnP77bfr0KFDmjhxogoKCtSpUyctW7ZM6ekV87179+5VQsLZK9ZffvllnTp1Srfeemulx5k0aZImT55s5tAB05xbyfF8W/+u5FRQ39jZlDN2hWNzyyYXOPXEz35AFQ+2ZnlyI0ljx46tdhpq9erVlW7v2bMn8gMCopCnkiNJ9eom6t4Fm0Kaqhr/161qkOxkB+cYUO42tHbXEY3/69aQ1quRpKd+0YGkFrZn+SJ+AALn2ZQzlG0cjp10acgr69jGIcp5tk0YMnedjp0Mfq2TjIbJVOsQN6KicgMgcOFqOi44syHnuJzWapl2gZo2YLrCSp5m4YPHv9eew6WauXJHSNNQNAsjHpHcADEsHE3Hng/OF1Z+7T1Go6k1aBYGwoPkBrAJmo5jG83CQPiQ3AA2QtNxbAnXejU0CwOVkdwANuVpOg5lmsPTdMwUR/iFcwoqg78foBKSG8DGPFNVa3cd0ZiFm4K+2oZpqvAKxxSUJDWq59SsIV2orAHn4VJwwOYSExzq0TpN02/pIIeC233IOPPn0SVbtWTzPuXvOqJyd6gfzfGn3G3os68Ph7RejSTv3+P0WzqoxxVpJDbAeajcAHEiHNNUbOMQPKahAPOQ3ABx5Nwrqs5dR0UKvOn4wJn1cVhHxbdwrVfjaQhnHSLAfyQ3QJw594oqSWqTUT+kisLcz/Zo7md7qOScgyoNYC2SGyDO0XQcXqxXA1iPhmIANB2HQTiahT2xf+oXHfSLzi2U3YqroIBgULkB4EXTcXDCNQ3FFBQQHiQ3ACphG4fAhGMaivVqgPAiuQFQBds41Czc2yZ41qsBEB4kNwBqxDYOlXElFBD9SG4A1Orcqaq8Lws077M9QVVyCs6sjRNra7Z4KjWe5x4M1qsBzENyA8Avnqmq7FYXqvtlTYKqXniSoRdWfu09Fu3VHJqFgdhDcgMgYPHSdEyzMBCbSG4ABMWuTcc0CwOxj+QGQMjs0nRMszBgDyQ3AMIi1rdxYNsEwD7YfgFA2MTiNg5smwDYD5UbAGEXK9s4cCUUYE8kNwAi4twrqg4e/157Dpdq5sodkoJbHyfcU1XhmIYa2aOlctpnMAUFRBmSGwARc+4VVZLUJqN+SOvjhHpFVbiuhIr2tXmAeEdyA8A0oTYdh3JFVahTUDQLA7GD5AaAqc5tOr53wSZJ4dvG4Xzh2jZBqmgWplIDxAaSGwCWCKXpuLptHCb2a+O9TbMwEL9IbgBYJtzbOIxbtEVPd5dWflWo0Qv/xbYJQJwiuQFgqXBu4+C5z5T3vmTbBCCORcUifrNmzVLLli2VnJysrKwsrV+/vsbz33rrLbVt21bJycnq0KGDli5datJIAUSSZ6oqo2FySI/zXempoO+b0TA5KjfxBOA/y5ObRYsWKTc3V5MmTdKmTZvUsWNH9enTRwcPHvR5/po1azRo0CCNHDlSmzdv1oABAzRgwAB9/vnnJo8cQCTcdFUzffrIDfrzyCw1quc05Xc2ucCpF27vpL+MukafPnIDiQ0Q4yxPbmbMmKFRo0Zp+PDhat++vWbPnq2UlBTNmzfP5/kvvviibrrpJj300ENq166dpk6dqi5duuj3v/+9ySMHECnh2MbBH2ybANiTpT03p06d0saNGzVhwgTvsYSEBOXk5Cg/P9/nffLz85Wbm1vpWJ8+ffT222/7PL+srExlZWXe28XFxZIkl8sllyu4jf3sxBMDYhFZxDk4N7ZJ00uDO2r6P7apoLj2q56SEoxK/61NRmqyxvdtqxvbpPF3EyBe0+YgzmcFEgNLk5vDhw+rvLxc6enplY6np6dr27ZtPu9TUFDg8/yCggKf50+bNk1TpkypcnzFihVKSUkJcuT2k5eXZ/UQ4gJxDk5u28DOn9rN7eeZJTq1e6OW7g54SDiD17Q5iLNUWlrq97m2v1pqwoQJlSo9xcXFyszMVO/evZWammrhyKKDy+VSXl6eevXqJafTnP6GeEScw2vlV4U+qzlJCYamdnPriQ0JKnNXnV7yVGpy2qVX+RkCw2vaHMT5LM/Miz8sTW7S0tKUmJiowsLCSscLCwuVkZHh8z4ZGRkBnZ+UlKSkpKQqx51OZ9y/UM5FPMxBnMOj79UXq/dVLardxqHM7VBZeUVyw7YJkcVr2hzEWQE9f0sbiuvWrauuXbtq1apV3mNut1urVq1Sdna2z/tkZ2dXOl+qKNdVdz4Ae6qt6ZhmYSB+WX61VG5urubMmaPXXntNX331le69916VlJRo+PDhkqShQ4dWaji+//77tWzZMj3//PPatm2bJk+erA0bNmjs2LFWPQUAFqpubRzWqwHil+U9N7fffrsOHTqkiRMnqqCgQJ06ddKyZcu8TcN79+5VQsLZHOzaa6/VwoUL9fjjj+vRRx9V69at9fbbb+uqq66y6ikAsJh3t/GdB3X4q7WaN+yHuuaKplRqgDhleXIjSWPHjq228rJ69eoqx2677TbddtttER4VgFiSmOBQ98uaaOlXorcGiHOWT0sBAACEE8kNAACwFZIbAABgKyQ3AADAVkhuAACArZDcAAAAWyG5AQAAtkJyAwAAbIXkBgAA2EpUrFBsJsMwJAW2dbqduVwulZaWqri4OO53nI0k4mwO4mweYm0O4nyW53Pb8zlek7hLbo4fPy5JyszMtHgkAAAgUMePH1fDhg1rPMdh+JMC2Yjb7db+/fvVoEEDORzsPVNcXKzMzEz95z//UWpqqtXDsS3ibA7ibB5ibQ7ifJZhGDp+/LiaN29eaUNtX+KucpOQkKCLL77Y6mFEndTU1Lj/h2MG4mwO4mweYm0O4lyhtoqNBw3FAADAVkhuAACArZDcxLmkpCRNmjRJSUlJVg/F1oizOYizeYi1OYhzcOKuoRgAANgblRsAAGArJDcAAMBWSG4AAICtkNwAAABbIbmJQ0ePHtWQIUOUmpqqRo0aaeTIkTpx4oRf9zUMQ3379pXD4dDbb78d2YHGuEDjfPToUf2///f/1KZNG9WrV0+XXHKJ7rvvPhUVFZk46ug3a9YstWzZUsnJycrKytL69etrPP+tt95S27ZtlZycrA4dOmjp0qUmjTT2BRLrOXPm6LrrrlPjxo3VuHFj5eTk1Pp3gwqBvqY93njjDTkcDg0YMCCyA4xBJDdxaMiQIfriiy+Ul5env//97/r444/1q1/9yq/7zpw5k20r/BRonPfv36/9+/frueee0+eff6758+dr2bJlGjlypImjjm6LFi1Sbm6uJk2apE2bNqljx47q06ePDh486PP8NWvWaNCgQRo5cqQ2b96sAQMGaMCAAfr8889NHnnsCTTWq1ev1qBBg/Thhx8qPz9fmZmZ6t27t/bt22fyyGNLoHH22LNnjx588EFdd911Jo00xhiIK19++aUhyfjnP//pPfaPf/zDcDgcxr59+2q87+bNm40WLVoYBw4cMCQZS5YsifBoY1cocT7Xm2++adStW9dwuVyRGGbM6d69uzFmzBjv7fLycqN58+bGtGnTfJ4/cOBAo1+/fpWOZWVlGf/7v/8b0XHaQaCxPt/p06eNBg0aGK+99lqkhmgLwcT59OnTxrXXXmu88sorxrBhw4yf//znJow0tlC5iTP5+flq1KiRunXr5j2Wk5OjhIQErVu3rtr7lZaWavDgwZo1a5YyMjLMGGpMCzbO5ysqKlJqaqrq1Im7beCqOHXqlDZu3KicnBzvsYSEBOXk5Cg/P9/nffLz8yudL0l9+vSp9nxUCCbW5ystLZXL5VKTJk0iNcyYF2ycn3zySTVt2pSqbg14x4wzBQUFatq0aaVjderUUZMmTVRQUFDt/caNG6drr71WP//5zyM9RFsINs7nOnz4sKZOner3lKHdHT58WOXl5UpPT690PD09Xdu2bfN5n4KCAp/n+/t3EK+CifX5HnnkETVv3rxKcomzgonzp59+qrlz52rLli0mjDB2UbmxifHjx8vhcNT4x983pfO9++67+uCDDzRz5szwDjoGRTLO5youLla/fv3Uvn17TZ48OfSBAyaaPn263njjDS1ZskTJyclWD8c2jh8/rjvvvFNz5sxRWlqa1cOJalRubOLXv/617rrrrhrPufzyy5WRkVGlUe306dM6evRotdNNH3zwgXbt2qVGjRpVOn7LLbfouuuu0+rVq0MYeWyJZJw9jh8/rptuukkNGjTQkiVL5HQ6Qx22LaSlpSkxMVGFhYWVjhcWFlYb04yMjIDOR4VgYu3x3HPPafr06Vq5cqWuvvrqSA4z5gUa5127dmnPnj3q37+/95jb7ZZUURnevn27WrVqFdlBxwqrm35gLk+j64YNG7zHli9fXmOj64EDB4ytW7dW+iPJePHFF41vvvnGrKHHlGDibBiGUVRUZFxzzTXGT37yE6OkpMSMocaU7t27G2PHjvXeLi8vN1q0aFFjQ/HPfvazSseys7NpKPZDoLE2DMN4+umnjdTUVCM/P9+MIdpCIHE+efJklffin//858YNN9xgbN261SgrKzNz6FGN5CYO3XTTTUbnzp2NdevWGZ9++qnRunVrY9CgQd6f//e//zXatGljrFu3rtrHEFdL1SrQOBcVFRlZWVlGhw4djJ07dxoHDhzw/jl9+rRVTyOqvPHGG0ZSUpIxf/5848svvzR+9atfGY0aNTIKCgoMwzCMO++80xg/frz3/M8++8yoU6eO8dxzzxlfffWVMWnSJMPpdBpbt2616inEjEBjPX36dKNu3brG4sWLK712jx8/btVTiAmBxvl8XC3lG8lNHDpy5IgxaNAgo379+kZqaqoxfPjwSm9Au3fvNiQZH374YbWPQXJTu0Dj/OGHHxqSfP7ZvXu3NU8iCv3ud78zLrnkEqNu3bpG9+7djbVr13p/9pOf/MQYNmxYpfPffPNN48orrzTq1q1r/OAHPzDef/99k0ccuwKJ9aWXXurztTtp0iTzBx5jAn1Nn4vkxjeHYRiG2VNhAAAAkcLVUgAAwFZIbgAAgK2Q3AAAAFshuQEAALZCcgMAAGyF5AYAANgKyQ0AALAVkhsAAGArJDcAAMBWSG4AAICtkNwAAABbIbkBYAslJSUaOnSo6tevr2bNmun5559Xz5499cADD1g9NAAmI7kBYAsPPfSQPvroI73zzjtasWKFVq9erU2bNlk9LAAWqGP1AAAgVCdOnNDcuXO1YMEC3XjjjZKk1157TRdffLHFIwNgBSo3AGLerl27dOrUKWVlZXmPNWnSRG3atLFwVACsQnIDAABsheQGQMxr1aqVnE6n1q1b5z323XffaceOHRaOCoBV6LkBEPPq16+vkSNH6qGHHtKFF16opk2b6rHHHlNCAt/fgHhEcgPAFp599lmdOHFC/fv3V4MGDfTrX/9aRUVFVg8LgAUchmEYVg8CACKhZ8+e6tSpk2bOnGn1UACYiJotAACwFZIbAABgK0xLAQAAW6FyAwAAbIXkBgAA2ArJDQAAsBWSGwAAYCskNwAAwFZIbgAAgK2Q3AAAAFshuQEAALby/wEpk/ApVcfmtAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "alpha, beta = 0.6, 1/3\n",
    "q, val, _ = phonoline(alpha, beta)\n",
    "val[(val < 0) & (val > -1E-6)] = 0\n",
    "\n",
    "plt.scatter(q, np.sqrt(val[:, 0]), marker='o')\n",
    "plt.scatter(q, np.sqrt(val[:, 1]), marker='o')\n",
    "plt.scatter(q, np.sqrt(val[:, 2]), marker='o')\n",
    "plt.xlabel('q')\n",
    "plt.ylabel('Energy')\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 关于 A-O 带隙的演化讨论\n",
    "\n",
    "这里固定 $ \\beta = 1/2 $, 可以解出当 $ \\alpha = \\frac{1}{2-\\beta} = \\frac{1}{2-1/2} = \\frac{2}{3} $ 时，\n",
    "A-O 带隙会恰好为 0 。通过观察声子谱的变化，可以发现始终存在一支能量为 $ \\omega = \\sqrt{\\beta} $ 的声子，\n",
    "它完全由质量比决定，与化学键的强度比无关；但是，还有一支随着化学键强度比强烈相关的声子，能量随着 $ \\alpha $ \n",
    "的增加而迅速。换言之，当材料的原子质量比确定时，要想显著降低 A-O 带隙，就必须要使得化学键的强度比小于阈值时，\n",
    "降低化学键强度才有意义。\n",
    "\n",
    "另外注意到 Gamma 点其中一个光学支的频率也仅依赖 $ \\beta $ (i.e., $ \\omega_o = \\sqrt{2+\\beta} $ )，\n",
    "这一特性可以方面我们量化前置约化系数 (D/M)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "beta_fixed = 1/2\n",
    "alpha_list = np.arange(0.1, 1.1, 0.05)\n",
    "num = len(alpha_list)\n",
    "val_list = []\n",
    "\n",
    "fig = plt.figure(figsize=(8, 5))\n",
    "cmap = plt.colormaps.get_cmap(\"viridis\")\n",
    "ax = plt.subplot(1, 2, 1)\n",
    "for i, alpha in enumerate(alpha_list):\n",
    "    q, val, _ = phonoline(alpha, beta_fixed)\n",
    "    val[(val < 0) & (val > -1E-6)] = 0\n",
    "    ax.scatter(np.tile(q, 3), np.sqrt(val.T.flatten()), s=3, color=cmap(i/num))\n",
    "    val_list.append(val[-1])\n",
    "ax.set_ylim(0, None)\n",
    "ylim = ax.get_ylim()\n",
    "\n",
    "ax2 = plt.subplot(1, 2, 2)\n",
    "val_list = np.sqrt(np.array(val_list))\n",
    "ax2.scatter(alpha_list, val_list[:, 0], c=alpha_list, cmap=cmap, s=8)\n",
    "ax2.scatter(alpha_list, val_list[:, 1], c=alpha_list, cmap=cmap, s=8)\n",
    "ax2.scatter(alpha_list, val_list[:, 2], c=alpha_list, cmap=cmap, s=8)\n",
    "ax2.set_ylim(ylim)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
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